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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.1
Linear system model for a signal
s
[
n
].
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.2
Inverse filter formulation for all
-
pole signal modeling.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.3
Linear prediction formulation for all
-
pole signal modeling.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.4
Linear system model for a random signal
s
[
n
].
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.5
Examples of deterministic and random outputs of a 1
st
-
order all
-
pole system.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.6
Illustration (for
p
= 5) of computation of prediction error for the autocorrelation method. (Square dots
denote samples of
h
A
[
n
−
m
] and light round dots denote samples of
s
[
m
] for the upper plot and
e
[
n
] for the lower plot.)
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.7
Illustration of computation of the autocorrelation function for a finitelength sequence. (Square dots denote
samples of
s
[
n
+
m
], and light round dots denote samples of
s
[
n
].)
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.8
Illustration (for
p
= 5) of computation of prediction error for the covariance method. (In upper plot, square
dots denote samples of
h
A
[
n
−
m
], and light round dots denote samples of
s
[
m
].)
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
All rights reserved.
Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.9
Illustration of computation of covariance function for a finite
-
length sequence. (Square dots denote
samples of
s
[
n
−
k
] and light round dots denote samples of
s
[
n
−
i
].)
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.10
Normalized mean
-
squared prediction error V
(p)
as a function of model order
p
in Example 11.2.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.11
(a) Windowed voiced speech waveform. (b) Corresponding autocorrelation function (samples connected
by straight lines).
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.12
(a) Comparison of DTFT and all
-
pole model spectra for voiced speech segment in Figure 11.11(a). (b)
Normalized prediction error as a function of
p
.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.13
(a) Windowed unvoiced speech waveform. (b) Corresponding autocorrelation function (samples
connected by straight lines).
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.14
(a) Comparison of DTFT and all
-
pole model spectra for unvoiced speech segment in Figure 11.13(a). (b)
Normalized prediction error as a function of
p
.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.15
Zeros of prediction error filters (poles of model systems) used to obtain the spectrum estimates in
Figure 11.12.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.16
Spectrum estimation for a sinusoidal signal.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.17
Equations defining the Levinson
–
Durbin algorithm.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.18
Comparison of the Levinson
–
Durbin algorithm and the algorithm for converting from
k
-
parameters of a
lattice structure to the FIR impulse response coefficients in Eq. (11.85).
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.19
Signal flow graph of prediction error computation.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.20
Signal flow graph of lattice network implementation of
p
th
-
order prediction error computation.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure 11.21
All
-
pole lattice system.
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.9
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.12
-
1
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.12
-
2
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.12
-
3
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.17
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.18
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.19
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Table 11.1
PREDICTION COEFFICIENTS FOR A SET OF LINEAR PREDICTORS
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.25
-
1
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.25
-
2
Lattice structure for 2
nd
-
order system
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.25
-
3
Lattice structure for 4
th
-
order system
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
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Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.27
-
1
Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc.
All rights reserved.
Discrete
-
Time Signal Processing
, Third Edition
Alan V. Oppenheim •
Ronald W. Schafer
Figure P11.27
-
2
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